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C₂³×#45002 #72325433

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1366360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

(7,8)(9,10)(11,12,14,15)(13,16,18,17)(19,20,23,25)(21,24,26,22);(8,9)(11,12)(13,17)(14,15)(16,18)(19,21)(20,24)(22,25)(23,26);(3,4);(5,6);(7,8,10,9)(12,15)(13,18)(20,25)(21,26);(1,2)(3,4)(5,6);(8,9)(11,12)(13,16)(14,15)(17,18)(19,21)(20,22)(23,26)(24,25);(7,9,10,8)(11,13)(12,16)(14,18)(15,17)(19,22)(20,21)(23,24)(25,26)

Conjugacy classes & character table

464 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((7,8)(9,10)(11,12,14,15)(13,16,18,17)(19,20,23,25)(21,24,26,22), (8,9)(11,12)(13,17)(14,15)(16,18)(19,21)(20,24)(22,25)(23,26), (3,4), (5,6), (7,8,10,9)(12,15)(13,18)(20,25)(21,26), (1,2)(3,4)(5,6), (8,9)(11,12)(13,16)(14,15)(17,18)(19,21)(20,22)(23,26)(24,25), (7,9,10,8)(11,13)(12,16)(14,18)(15,17)(19,22)(20,21)(23,24)(25,26));